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Steady-state $GI/GI/n$ queue in the Halfin-Whitt Regime

Series:

Stochastics Seminar

Thursday, September 29, 2011 - 15:05

1 hour (actually 50 minutes)

Location:

Skiles 006

Speaker:

David Goldberg

,

ISyE, Georgia Tech

In this talk, we resolve several questions related to a certain heavy
traffic scaling regime (Halfin-Whitt) for parallel server queues, a family
of stochastic models which arise in the analysis of service systems. In
particular, we show that the steady-state queue length scales like
$O(\sqrt{n})$, and bound the large deviations behavior of the limiting
steady-state queue length. We prove that our bounds are tight for the
case of Poisson arrivals. We also derive the first non-trivial bounds for
the steady-state probability that an arriving customer has to wait for
service under this scaling. Our bounds are of a structural nature, hold
for all $n$ and all times $t \geq 0$, and have intuitive closed-form
representations as the suprema of certain natural processes. Our upper
and lower bounds also exhibit a certain duality relationship, and
exemplify a general methodology which may be useful for analyzing a
variety of stochastic models. The first part of the talk is joint work
with David Gamarnik.